Unraveling the electronic influence and nature of covalent bonding of aryl and alkyl radicals on the B12N12 nanocage cluster

Carbon nanocage structures such as fullerene, nanotubes, nanocapsules, nanopolyhedra, cones, cubes, and onions have been reported since the discovery of C60, and they offer tremendous promise for investigating materials of low dimensions in an isolated environment. Boron Nitride (BN) nanomaterials such a: nanotubes, nanocapsules, nanoparticles, and clusters have been described in several studies and are predicted to be useful as electronic devices, high heat-resistance semiconductors, nanocables, insulator lubricants, and gas storage materials. The interaction, and electronic of octahedral B12N12 nanocage cluster covalently modified from the attachment of alkyl and aryl radicals were analyzed using Density Functional Theory calculations. The work discusses for the first time to our knowledge the complete investigation of the impact of the grafted aryl and alkyl groups on the electronic, bang gap, and density of states on the B12N12. Furthermore, this is the first complete description of these radicals attaching to a surface of B12N12 nanocage cluster.


Results and discussion
Bond lengths and adsorption energies. Figure 1 depicts the B 12 N 12 optimized structure at the B3LYP[/ def2tzvp basis set. B 12 N 12 structure has been optimized. In this cluster, the nitrogen and boron sites are equal. Six tetragonal (4-membered) and eight hexagonal (6-membered) rings make up the cluster. The length of the BN bond varies depending on whether the bond is between a tetragonal and a hexagonal ring (b 64 ) or between two hexagonal rings or between two hexagonal rings (b 66 ) 6,40 . The length of the BN bond shared by two hexagonal rings (b 66 ) is 1.43783 Å, whereas the length of the BN bond shared by a tetragonal and a hexagonal ring (b 64 ) is 1.48422 Å.
Grafting aryl and alkyl groups onto the BN cage, in general, induces alterations in the geometry of the BN cage. When these groups are present on the link between two hexagonal rings (atom N 2 -B 24 ), the length of the BN bond increases in all cases of the grafted moieties as presents in Table 1. This is also seen to be the case for the BN bonding that exists between the tetragonal rings (atoms N 4 -B 24 ). These induced structural alterations caused by radical grafting have previously been documented in gold clusters and other materials 25,41 . The bond between the grafted B24 atom of the B 12 N 12 nanocage cluster and the C atoms of aryl or alkyl groups is close to the previously reported experimental value for B-C bond of d (B-C) = 1.534 ± 0.01 Å indicating that these moieties are strongly covalently bound to the clusters surface 42 .
We investigated the reactions that the aryl radicals (phenyl and nitrophenyl) and the alkyl radical (hexyl) had with the B 12 N 12 nanocage cluster. It has been previously confirmed that the Bond Dissociation Energy (BDE) is a significant parameter that can be used to evaluate the strength of the interface while the grafting process is taking place 25,26,41,[43][44][45][46] .
The calculated BDEs for the grafted groups as shown in Fig. 2 were more than 60 kcal/mol. These numbers are suggestive of the establishment of an interface that is stable 43 . The layers generated by grafting radicals are more stable than previously documented surface modification processes based on the formation of self-assembling monolayers (SAM) through thiol chemistry (BDE|Au-S-(CH 2 ) 5 -COOH|= 31.59 kcal/mol).
Dipole moment. The dipole moments of pure B 12 N 12 and grafted B 12 N 12 were compared and are shown in Table 2. The pure B 12 N 12 cage has no dipole moment since it is symmetrical 40 . Binding of a-Ph, -C 6 H 12 , or PhNO 2 group raises the dipole moment in B 12 N 12 -Ph from zero to 2.237 D, accordingly to 6.666 for -PhNO 2 , but grafting of a -alkyl group (-C 6 H 12 ) results in just a minor increase of the dipole moment up to 0.882.  www.nature.com/scientificreports/ This effect is important as not only alters the electronic properties as seen above but also it enables the dispersibility in different solvents 22 . These alterations are ascribed to aryl or alkyl group additions, which disrupt charge separation in the B12N12 nanocage. The dipole moment vectors (Fig. 2) in the grafted structures, as shown in Fig. 3, point from the grafted groups toward the B 12 N 12 or vice versa, suggesting charge transfer from these groups to the nanocage or the inverse.

MEP analysis.
To understand the interaction between the B 12 N 12 and the grafted aryl or alkyl group, the molecular electrostatic potential (MEP) is performed. It represents the extent of charge dispersion in a molecule and relates molecular structure to physiochemical qualities such as chemical reactivity, dipole moment, and partial charges.
The electron-deficient blue area (in the online version) in Fig. 4 represents boron atoms, whereas the electronrich yellow zone represents nitrogen atoms. Because the pure B 12 N 12 nanocage is symmetrical, it exhibits both charges to an equal amount, which alter somewhat following the grafting of alkyl or aryl groups. These groups after their grafting reduce the intensity of the blue zone on the B 12 N 12 nanocage (shifting toward the grafted moieties).   www.nature.com/scientificreports/ Electronic properties. The influence that the grafted groups have on the B 12 N 12 nanocages can be seen rather well when looking at the densities as well as the electronic energy levels. Figure 5 provides details about a variety of orbital properties, including the energies of the HOMO and LUMO states as well as the HOMO-LUMO band gap (Eg). The B 12 N 12 nanocage is a semiconductor with a HOMO LUMO gap (Eg) of 6.752 eV. The B 12 N 12 nanocage has HOMO and LUMO values of − 7.92 and − 1.17 eV, respectively. The Fermi level, EFL, is equal to − 4.54 eV. The Fermi level denotes the center of the HOMO-LUMO energy gap (in a molecule when the temperature is 0 K). The grafting of carbon-centered radicals onto a nanocage alters the HOMO and LUMO energies and consequently the band gap of this entity. The band gap difference is reduced in all grafted instances. The HOMO-LUMO gap (Eg) is directly related to conductivity, resulting in a high energy level for the newly generated HOMO 47 . As a result of the narrowing of the energy gap between the HOMO and LUMO states, it is anticipated that there would be a significant increase in the material's electrical conductivity (Eg). This will make it possible for the resultant grafted clusters to be utilized in novel ways (electronics, photovoltaic applications, sensing, …). The DFT results were used to calculate the band gap energy and the threshold wavelength 48 . The Tauc plot generated from DFT calculations in the gas phase and the corresponding optical band gap values can be found in the Supporting Information (Fig. S1 and Table S1) 49 . The optical bang gap as observed in many studies is often much lower than the fundamental HOMO-LUMO gap because, in the excited state (as opposed to the ionized state), the electron and hole remain electrostatically coupled to one another 50 .
Partial density of states (PDOS). The structural alterations and electrical characteristics of bare B 12 N 12 and B 12 N 12 nanocages after grafting were investigated using partial density of states (PDOS). As shown in Fig. 6, the LUMO has density primarily localized grafted groups in the case of B 12 N 12 -PhNO2, on the entire structure for B 12 N 12 -Ph, and almost on the B 12 N 12 nanocage for B 12 N 12 -C 6 H 13 ; the HOMO is centered only on the grafted phenyl groups, whereas in the case of B 12 N 12 -C 6 H 13 it is also in the vicinity of the grafted.

Quantum theory of atoms in molecules (QTAIM). Electron density analysis was performed in the
context of Bader's proposed quantum theory of atoms in molecules (QTAIM) 51,52 . In general, the electron density at the Bond Critical Points (BCP), ρ (b) , is greater than 0.20 e − bohr −3 in shared-shell interactions, i.e., covalent bonds, and less than 0.10 e − bohr −3 in closed-shell interactions (e.g. ionic, van der Waals, hydrogen bonding) 53,54 .
The binding among the atoms on the grafted structures is visible in Fig. 7, by analyzing the presence of the Bond Critical Points (BCPs)-presented as green spheres. As seen in Table 3, ρ(b) is close to 0.2 e − bohr −3 , indicating that the formed B-C bond has some polarization due to differences in electronegativity among the bonded atoms [χ(C) = 2.5 and χ(B) = 1.5].
Another energetic descriptor that is frequently used to distinguish two types of closed-shell bonding is the |Vb|/Gb ratio, which reflects the covalency magnitude of the interaction. If the latter ratio is less than one, the kinetic energy density is the leading term, and electrons are destabilized near the BCP, implying that no covalency is expected (for example pure ionic or van der Waals bonding). These interactions are referred to as pure closed-shell interactions (pure CS). The second type of closed-shell bonding involves some electron sharing (|Vb|/Gb > 1, indicating that the potential energy density is high and electrons are stabilized at the BCP) 54,55 . In the case of B 12 N 12 grafted cluster the |Vb|/Gb is > 1 indicating that there is a close shell type of bonding with electron some sharing. The delocalization index, DI, or δ(Ω,Λ) is a quantitative tool used to assess the extent of electron sharing in the context of QTAIM. DI is close to zero for an ideal ionic system, but close to unity for homo-nuclear covalently bonded systems, two for double bonds, and so on 56 . It is a direct measure of electron sharing that reflects covalency. This supports the fact that the B-C bond has a covalent-polarized character. www.nature.com/scientificreports/ ELF. In order to gain a better understanding of the nature of the new covalent chemical bonds that are forming between the carbon atom on the alkyl or aryl radical and the boron atom that is a part of the B 12 N 12 nanocage cluster, we have further calculated the Electron Localization Function (ELF) 23,57 . By establishing a renormalization of the Fermi hole curvature, the ELF serves as a measure for electron pairing (localization). Values for the ELF range from zero (no electron localization) to one, with zero indicating that there is no electron localization and one indicating that there is complete electron localization (electron pairing, covalent bond). Covalent bonding may be recognized in Fig. 8 as the maxima of ELF occurring along the bond almost halfway between the two atoms (B-C). It is evident from the ELF depicted in Figure that the bonding between the two atoms in question is of the covalent type. As seen in this figure, the presence of a red region in the center of two carbon atoms demonstrates that the B-N bond on the nanocluster is actually of the covalent nature. These results are supported also through the analysis of the bond order: Mayer Bond order 58,59 , Fuzzy Bond Order (FBO) 60 and Laplacian Bond Order (LBO) 61 between the bonded atoms as presented in Table 4.
The electron density is split in such a way by the Mayer bond order that the degree of bonding can be determined in a straightforward manner. According to this order, the value assigned to a completely fulfilled double bond is 2, the value assigned to a triple bond is 3, and so on 62 . The bond order values are rather near to one, showing once more the presence of covalent single bonds between the B-C atoms of the grafted moieties, as opposed to multiple bonds. In order to be independent of the calculation methods (the usage of basis set), the FBO were also computed; typically, the magnitude of the FBO is similar to the Mayer bond order, particularly for low-polar bonds, but is considerably more stable with regard to the change in basis set. LBO presented a new concept of covalent bond order based on the Laplacian of electron density ∇ 2 ρ in fuzzy overlap space 61 . LBO was shown to be logical and helpful by applying it to a wide range of compounds and comparing it to various current bond order classifications. It is demonstrated that LBO has a direct relationship with bond polarity, bond dissociation energy, and bond vibrational frequency. LBO has a low computational cost and is indifferent to the computing level utilized to create electron density. The numbers corroborate the atom bonding order; the calculated values are quite near to Mayer bond orders. www.nature.com/scientificreports/ Electron density difference (EDD) analysis. When a chemical bond is formed, an important rearrangement of the electrons in the system takes place, which results in polarization and the transfer of charge. In particular, the creation of a covalent bond must be accompanied by the phenomena of electrons congregating in the bonding area. This may be shown by plotting an electron density difference (EDD) plot, which is one of the most effective ways to do so. In the Fig. 9, we can observe that the interaction includes charge transfer mostly between the C atom and the surrounding B atoms in B 12 N 12 by referring to the charge density difference diagrams of aryl or alkyl groups and B 12 N 12 cluster. EDD show that there is a concentration of electron density (red color in map) between C and B atom supporting the bond formation. Additionally, the formation of a chemical connection between two distinct fragments must result in measurable charge transfer (CT). CT may be calculated as the difference between the fragment charge in the actual system and the net charge of the fragment in its isolated condition. The fragment charge is defined as the total of the charges of the fragment's atoms 37 . It's worth noting that the amount of charge regarding the charge fragments of the various bound groups differs, for:-C 6 H 13 (q = − 0.0237),-Ph (q = 0.091) and -PhNO 2 (q = − 0.151)-this is probably what influences the BDE values and the Bond orders for the B-C atoms.

Conclusion
We used the DFT calculations to investigate the grafting of aryl and alkyl radicals on B 12 N 12 nanocages in this work. The computed BDEs for the grafted groups were greater than 60 kcal/mol, indicating the formation of a stable interface. After grafting, B 12 N 12 exhibits significant changes in its electronic properties. The dipole moment  www.nature.com/scientificreports/ of the grafted system increases as well. The HOMO/LUMO gap in bare B 12 N 12 is greater than in other grafted systems. Furthermore, the partial density of states and electronic energy level were computed to demonstrate the influence of the grafted moieties on the structure of B 12 N 12 . The ELF, QTAIM, EDD, CT and bond order all clearly demonstrate that the generated bond between the B atom of the B 12 N 12 and the grafted aryl or alkyl groups is polarized covalent.

Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.